Not only Arsenal, I think injury problems will always be a scourge for any team, especially if it has entered the middle of the season. With the fall of Arsenal in the FA Cup, I thought they would have had more time to rest than their closest competitors. So Man City and Man United should also be careful because they have a tighter schedule of matches than Arsenal and Newcastle.
You are right and I agree that with so many choices rest has the potential to stabilize players. Especially Arteta did not want to take any further risks. I'm sure what Arsenal gets knocked out in the FA Cup will be very beneficial in the Premier League and only focus on maintaining the Standings. It's no wonder that clubs like Manchester United and Manchester City will be preoccupied with busy schedules and players with a higher potential for injury. If that does happen at least a plus point for Arsenal to be in full control.
Arsenal eliminated from the FA Cup reduced the number of competitions they participated in, the Arsenal could focus more on the EPL and UEL as targets to be achieved at the end of the season. Arsenal also avoided a busy schedule that often injured players due to fatigue. Arteta could minimize the risk of injury to his players by focusing on just two competitions.
Arsenal are now focusing on the Premier League after winning 5 points from Manchester City, Arsenal chances are very open to maintain their position until the end of the season. Arteta can rotate when his team has the upper hand against weak teams, he can withdraw the main players to give him more hours of rest and keep his condition fit so that he is better prepared when playing in big matches.